The Co-op said it would no longer advertise products that were high in fat, sugar and salt during children's television programmes.
Research commissioned by the company found that advertisers push such products particularly strongly when they know children are watching.
The Co-op is also boycotting the use of character and cartoon merchandising on the same Co-op products, and has pledged to promote healthy diets to children.
The company wants the Independent Television Commission to force others in the food industry to follow its lead.
The Co-op said it was prompted to take action after successive government health warnings about poor nutrition in children's diets.
It commissioned a survey into food commercials aimed at youngsters, which found that 99% of food and drink advertised to children during Saturday morning children's television contained either high fat, high sugar, or high salt.
Adverts for cakes, biscuits, and confectionery constituted 46% of advertising on Children's ITV (CITV) and 53% on the Big Breakfast, compared with a combined figure of just 13% on evening television.
Brain effect
"There are now concerns that the short, high stimulation nature of TV commercials for children may have permanent effects on their brain development and their attention spans."
The inquiry identified several ways that advertisers sought to appeal to children, which included making products appear to be their friend, using animation, celebrities or heroes, and encouraging them to collect things and compete.
Researchers also discovered that 73% of children asked their parents to buy things they had seen advertised on television and that 77% of parents wanted to see a ban on this type of commercial.
Co-op spokeswoman Wendy Wrigley said: "Our findings clearly demonstrate that the combined impact of food and drink advertising during children's TV viewing hours runs counter to both the government's healthy eating guidelines and the spirit of the ITC code.
"Our customers - parents in particular - are crying out for action to be taken against the mass advertising of these products to children, which is why we're campaigning for an all-out ban."
But the Food and Drink Federation, which represents food manufacturers in the UK, said there were already codes of practice governing children's advertising.
A spokesman said: "These state that ads should not encourage children to eat or drink frequently throughout the day, condone excessive consumption, or suggest that confectionery or snacks should replace balanced meals.
"As for pester power, studies have shown that parents in Sweden - where advertising to children is banned - complain more about children pestering them to buy things than they do in Spain where advertising is completely deregulated."